Question

How do I write these circles in standard form?

Answer 1

Check the picture below.

`\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{small}{circle}~~ \begin{cases} r=2\\ h=0\\ k=0 \end{cases}\implies (x-0)^2+(y-0)^2=2^2\implies x^2+y^2=4 \\\\\\ \stackrel{large}{circle}~~ \begin{cases} r=3\\ h=5\\ k=-4 \end{cases} \\[3em] [x-5]^2+[y-(-4)]^2=3^2\implies (x-5)^2+(y+4)^2=9`

Answer 2

A:
`(x-0)^(2) +(y-0)^(2) = 2^(2)`

or
`x^(2) +y^(2) =4`

B:
`(x-5)^(2) +(y+4)^(2) =9`